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a(n) = n - A075860(n).
0

%I #8 Aug 28 2024 11:26:05

%S 1,0,0,2,0,1,0,6,6,3,0,7,0,11,13,14,0,13,0,13,14,9,0,19,20,24,24,25,0,

%T 23,0,30,30,15,30,31,0,31,37,33,0,37,0,31,43,41,0,43,42,43,44,50,0,49,

%U 53,53,44,27,0,53,0,59,56,62,60,64,0,49,67,67,0,67,0,72,73,69,72,73

%N a(n) = n - A075860(n).

%C If p is a prime number, then a(p)=0.

%e For n=15, a(15) = 15-2 = 13.

%p f := proc(n)

%p option remember:

%p if isprime(n) then

%p n

%p else

%p procname(convert(numtheory:-factorset(n), `+`))

%p end if

%p end proc:

%p f(1) := 0:

%p seq(n - f(n), n = 1..100);

%o (Python)

%o from sympy import primefactors

%o def a(n, pn):

%o if n == pn:

%o return n

%o else:

%o return a(sum(primefactors(n)), n)

%o print([i-a(i, None) for i in range(1, 100)])

%Y Cf. A075860.

%K nonn

%O 1,4

%A _Rafik Khalfi_, Aug 18 2024